What is the answer to ((x-1))/(2-x)=i ?

The answer to ((x-1))/(2-x)=i is x= 3/2+1/2 i

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((x-1))/(2-x)=i

\frac{( x - 1 )}{2 - x} = i

x = \frac{3}{2} + \frac{1}{2} i

Solution steps

\frac{( x - 1 )}{2 - x} = i

Substitute

x = a + bi

\frac{a + bi - 1}{2 - ( a + bi )} = i

Multiply both sides by

2 - a - ib

\frac{a + bi - 1}{2 - ( a + bi )} (2 - a - ib) = i (2 - a - ib)

Expand

(a - 1) + ib = b + i (2 - a)

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[a - 1 = b b = 2 - a]

[a - 1 = b b = 2 - a] : a = \frac{3}{2}, b = \frac{1}{2}

Substitute back

x = a + bi

x = \frac{3}{2} + \frac{1}{2} i

x y + (x - y) i = 4

∣ z - 1 - i ∣ = 1

x^{2} + 2 (1 + i) x - 5 (1 + 2 i) = 0

i (x) = \frac{640000}{4 - 4}

s i f (x) = 2 - 3 x^{2}

What is the answer to ((x-1))/(2-x)=i ?
The answer to ((x-1))/(2-x)=i is x= 3/2+1/2 i